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Math Help - Easy integral help

  1. #1
    MHF Contributor arbolis's Avatar
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    Easy integral help

    Can you tell me an easy way (or some easy ways) to solve the following integral? \int\frac{dx}{sin^2(x)}
    Thanks.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by arbolis View Post
    Can you tell me an easy way (or some easy ways) to solve the following integral? \int\frac{dx}{sin^2(x)}
    Thanks.
    Hint: Note that \int \frac {dx}{\sin^2 x}~dx = \int \csc^2 x ~dx

    what do you differentiate to get csc(x)?
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  3. #3
    MHF Contributor arbolis's Avatar
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    I don't remember... I guess there is a ln of something.
    So let's solve the simpler integral  \int \frac{1}{sin(x)} dx. To get the one I need, I think a simple substitution will do the job.
    I thought of integration by part, but it get more complicated than  \int \frac{1}{sin(x)} dx. Can you help me a little more?
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  4. #4
    Behold, the power of SARDINES!
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    Quote Originally Posted by arbolis View Post
    I don't remember... I guess there is a ln of something.
    So let's solve the simpler integral  \int \frac{1}{sin(x)} dx. To get the one I need, I think a simple substitution will do the job.
    I thought of integration by part, but it get more complicated than  \int \frac{1}{sin(x)} dx. Can you help me a little more?
    to make Jhevons hint more explicit

    what is \frac{d}{dx}\cot(x)

    This may help...
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  5. #5
    Super Member PaulRS's Avatar
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    Quote Originally Posted by arbolis View Post
    Can you tell me an easy way (or some easy ways) to solve the following integral? \int\frac{dx}{sin^2(x)}
    Thanks.
    Ok, if you don't see it directly try: u=\tan(x) it's very straightforward
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  6. #6
    MHF Contributor arbolis's Avatar
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    what is
    , I got \frac{-1}{sin^2(x)}, therefore \int\frac{dx}{sin^2(x)}=-cot(x). Thanks a lot for your help.
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